Exponential splines difference scheme for singular perturbation problem with mixed boundary conditions

Abstract

We generate an exponential splines difference scheme for a one-dimensional singularly perturbed self-adjoint problem along with general boundary conditions of the third kind. We obtain O(h min(h,√ε)) accuracy if one has Dirichlet's boundary conditions on the right end point, and order one in the remaining cases. These results are supported by numerical experiments.